Method of locking 1alpha-OH of vitamin D compounds in axial orientation

ABSTRACT

A method of modifying or altering the structure of a 1α-hydroxylated vitamin D compound to increase its biological activity by altering the conformational equilibrium of the A-ring to favor a chair conformation that presents the 1α-hydroxyl in the axial orientation. This is accomplished by either locking the A-ring chair conformation in a geometry having an axially orientated 1α-hydroxyl, or by the addition of one or more substituents to the A-ring which interact with other substituents in the molecule or on the A-ring to provide a driving force to the A-ring to adopt a chair conformation which presents the 1α-hydroxyl in the axial orientation.

STATEMENT REGARDING FEDERALLY SPONSERED RESEARCH OR DEVELOPMENT

[0001] This invention was made with United States government support awarded by the following agencies:

[0002] NIH Grant No. DK14881

[0003] The United States has certain rights in this invention.

BACKGROUND AND SUMMARY OF THE INVENTION

[0004] The present invention relates to vitamin D compounds, and more particularly, to a method of presenting the 1α-OH of vitamin D compounds in an axial orientation and the compounds made thereby.

[0005] The two diastereomeric forms of monosubstituted cyclohexanes (Scheme I) are differently populated, the equilibrium constant K being given by the equation

ΔG°=−RT1nK

[0006] where K=[equatorial conformer]/[axial conformer]. ΔG° (usually negative) is the difference of free energy between the equatorial and axial conformers and −ΔG° is known as conformational free energy of the substituent R [defined as it's A value, Winstein et al., J. Am. Chem. Soc. 77, 5562 (1955)]. Thus, the greater the A value of the substituent R, the greater a driving force to adopt the R-equatorial form. A value can be, therefore, considered as

[0007] destabilization energy imparted to a monosubstituted six-membered chair by an axial substituent. Thus, for example, the A value of methyl substituent equals ca. 1.7 kcal/mol [Hirsch, Top. Stereochem. 1, 199 (1967)] that corresponds to 95% of population of equatorial conformer of methylcyclohexane at room temperature. The conformational free energies of substituents in cyclohexanes under ideal conditions are expected to be additive. It is usually assumed that all conformational effects are additive, i.e. various destabilizing interactions identified within a six-membered ring system operate independently of each other. In di-, tri- and polysubstituted cyclohexanes mutual interactions among the substituents have to be considered. Such interactions can destabilize one chair conformation raising its energy to favor an alternate inverted chair form, or even favor some other, distorted (rigid or flexible) cyclohexane geometries. The most important interactions that influence the equilibrium between the respective chair conformations include interaction of a pair of substituents in 1,2-trans-diequatorial and 1,3-cis-diaxial relationship. Thus, total destabilization energy (E_(D)) can be described as a sum of the substituents' A values, representing monoaxial interactions, G values for 1,2-diequatorial interactions and U values for 1,3-diaxial interactions [Corey, et al., J. Org. Chem. 45, 765 (1980)].

E_(D)=Σ(A+G+U)

[0008] In the case of alkylidenecyclohexanes, additional interactions are involved, especially in 2-substituted derivatives. The most important interaction (designated A^(1,3)-strain, Johnson, Chem. Rev. 68, 375 (1968)] exists in the allylic segment between equatorial R₁ and substituent R₂ of the exomethylene unit (Scheme II). When both

[0009] R₁ and R₂ are medium or large groups, the axial conformer is preferred over the equatorial (Malhotra et al., J. Am. Chem. Soc. 87, 5492 (1965)]. Thus, for example, when R₁=R₂=Me the difference in energy between both forms is approximately 4.5 kcal/mol, in favor of the axial conformer. In the case when R₁=Me and R₂=H, a 1:3 peri interaction exists which increases by ca. 1.25 kcal/mol the destabilization energy of the system (Duraisamy et al., J. Am. Chem. Soc. 105, 3264 (1983)].

[0010] Conformational behavior of vitamin D has attracted considerable attention over the past 25 years. It has been suggested long ago [Havinga, Experientia 29, 1181 (1973)] that vitamin D compounds can exist as a mixture of two rapidly equilibrating A-ring chair conformers. These two conformations were abbreviated as α- and β- forms (Scheme III). ¹H NMR studies of vitamin D₂ and D₃ in chloroform solutions confirmed the existence of the dynamic equilibrium between the two chair forms [La Mar et al., J. Am. Chem. Soc. 96, 7317 (1974); Wing et al., J. Am. Chem. Soc. 97, 4980 (1975)] of these B-ring secosteroids. A similar conformational equilibrium has also been found for 25-hydroxyvitamin D₃ (25-OH-D₃), 1α-hydroxyvitamin D₃ (1α-OH-D₃) and the natural hormone 1α,25-dihydroxyvitamin D₃ (1α,25-(OH)₂D₃) as well as some other A-ring substituted vitamin D derivatives [see for example Helmer et al., Arch. Biochem. Biophys. 241, 608 (1985); Sheves et al., J. Org. Chem. 42, 3597 (1977); Berman et al., J. Org. Chem. 42, 3325 (1977); Sheves et al., J. Chem. Soc. Chem. Commun. 643 (1975); Okamura et al., J. Org. Chem. 43, 574 (1978)]. In the α-chair conformer of vitamin D molecule, the hydroxy group is equatorial whereas in the β-chair conformer the hydroxy group is axially oriented.

[0011] NMR studies of various vitamin D compounds in solutions have also shown that the ratio of the respective A-ring conformers depends significantly on the solvent used [Helmer et al., Arch. Biochem. Biophys. 241, 608 (1985)]. Unfortunately, due to solubility problems, it is impossible to study these conformer populations in an aqueous medium. X-Ray diffraction studies of vitamin D₂ and D₃ confirmed that their A-rings also occur in the solid phase as an equimolar mixture of such extreme α- and β-chair conformations [Hull et al., Acta Cryst., Sect. B, 32, 2374 (1976); Trinh et al., J. Org. Chem. 41, 3476 (1976)]. Interestingly, 25-OH-D₃ exists in the solid state exclusively in the α-form whereas the natural hormone 1α,25-(OH)₂D₃ in the A-ring β-form [Trinh et al., J. Chem. Soc., Perkin Trans. II, 393 (1977); Suwinska et al., Acta Cryst., Sect. B, 52, 550 (1996)]. X-Ray studies have also shown that the C(5)═C(6)-C(7)═C(8) diene part of the molecule is nearly planar, whereas the exocyclic C(10)═C(19) bond, because of steric strain, is twisted out of plane by about 55°. This exomethylene group is situated below the mean A-ring plane in the α-chair form and above it in the alternate β-chair form. In the case of vitamin D analogs substituted in the ring A with a 1α-hydroxy group, crucial for biological activity, the orientation of 1α-OH is axial in the α chair form and equatorial in the β-form (Scheme IV).

[0012] It has to be added that molecular mechanics calculations revealed that, similarly as in the case of the model 1,2-dimethylenecyclohexane ([Hofmann et al., J. Org. Chem. 55, 2151 (1990)], an existence of other than low-energy chair conformations of the ring A can be expected for D vitamins, namely, half-chair or twist forms [Mosquera et al., J. Mol. Struct. 168, 125, (1988); Hofer et al., Monatsh. fur Chemie, 124, 185 (1993)].

[0013] In 1974, it was proposed [Okamura et al., Proc. Natl. Acad. Sci. USA 71, 4194 (1974); Wing et al., Science 186, 939 (1974)] that calcium regulation ability of vitamin D is limited to the compounds that can assume a ring-A chair conformation in which the 1α-hydroxy group (or pseudo-1α-OH) occupies an equatorial orientation. Such conformation, according to this hypothesis, has the proper geometry for binding to the protein receptor, a step which is necessary to induce the biological response leading to the calcium transport and calcium mobilization in the body. However, recent results of biological testing of 1 α,25-dihydroxy-10, 19-dihydroxyvitamin D₃ compounds do not support the idea that the equatorially favored 1-hydroxyl would be the most biologically active. On the contrary, 1α,25-dihydroxy-10(S), 19-dihydrovitamin D₃, the analog strongly biased toward the A-ring chair conformer possessing 1α-axial orientation, provided the greatest in vivo biological response and showed very significant activity on intestinal calcium transport. Moreover, more recent studies on 19-norvitamins, especially those substituted at C-2, demonstrate that pronounced biological activity is provided by compounds having an axial 1α-hydroxyl. Thus, it is believed that axial orientation of the 1α-hydroxyl group in the vitamin D molecule is of crucial importance for its biological activity and, the prediction of its biological response can be made by evaluation of the conformational equilibrium of the A-ring of the vitamin. It is believed that the more favored the axial position of 1 α-hydroxyl is the greater biological response can be expected. A logical extension of this prediction is that the greatest activity can be predicted for such A-ring substitution of vitamin D molecules which:

[0014] 1) constitute anancomeric system or other corresponding to at least 90% preponderating conformer possessing 1α-OH in axial position, even though the rate of A-ring inversion can remain facile—these analogs are characterized by conformationally free well-defined geometries of A rings and a significant energy advantage (at least 1.2 kcal/mole) for an axial 1α-OH conformer; or 2) constitute conformationally locked, rigid or distorted geometries in which the A ring is held in only one chair conformation, i.e. the one having an axial 1α-OH or, although it may deform considerably, it may not flip over to its conformationally inverted opposite form with equatorial orientation of 1α-OH.

[0015] Such structural constrains which prevent the cyclohexane ring from flipping but which can be accommodated by its chair geometry (Scheme V) include:

[0016] 1) anchoring bonds (trans-fasion bonds to a ring of size seven or smaller),

[0017] 2) flattening bonds (fusion bonds to a ring of size seven or smaller which contains a double bond exocyclic to the six-membered ring), and

[0018] 3) bridged bonds (two contiguous ring bonds whose termini are joined by a bridge of five atoms or fewer).

[0019] It should be noted that the remaining substituents (or hydrogens) of flattening or anchoring bonds must assume an axial orientation with respect to the six-membered ring. In the case of (1,3)-bridging, the bridged bonds have to be axially disposed with respect to the six-membered ring.

[0020] Accordingly, the present invention provides a novel class of 1α-hydroxylated vitamin D compounds wherein the conformational equilibrium of the A-ring has, or has been altered or modified to favor a chair conformation that presents the 1 α-hydroxyl in the axial orientation, and the A-ring is attached to the conventional 5,7-diene and C-D ring system having any known side chain attached at carbon 17 of the D-ring.

[0021] Structurally these novel analogs are characterized by the general formula I shown below:

[0022] where Y₁ and Y₂, which may be the same or different, are each selected from the group consisting of hydrogen and a hydroxy-protecting group; where Y₃, Y₄, Y₅, Y₆, Y₇ and Y₈, which may be the same or different, are each selected from the group consisting of hydrogen, a methyl group or substituted methyl group of the formula —CR₁R₂R₃, an amino group or substituted amino group of the formula —NR₁R₂, a phosphino group or substituted phosphino group of the formula —PR₁R₂, an alkylsulfinyl group, an arylsulfinyl group, an alkylsulfonyl group, an arylsulfonyl group, and aryl, where R₁, R₂ and R₃ are each independently selected from the group consisting of hydrogen, C₁₋₅ alkyl, hydroxyalkyl, aminoalkyl, halogenalkyl, alkoxyalkyl, aryloxyalkyl, aryl, halogen, hydroxyl, protected hydroxy, alkoxyl, aryloxyl, acyl, an amino group, an alkyl substituted amino group, and an aryl substituted amino group, and where R₁ and R₂ taken together represent an oxo group or a group —(CH₂)_(m)- where m is an integer having a value of from 2 to 5; or Y₃ and Y₄ when taken together represent a methylene group; or Y₇ and Y₈ when taken together represent a methylene group; where Y₂ and Y₆, or Y₂ and Y₇, when taken together may represent the group —(CR₁R₂)_(n)- where n is an integer having a value of from 1 to 4 and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom; where Y₅ and Y₈, or Y₅ and Y₃, or Y₃ and Y₈, when taken together may represent the group —(CR₁R₂)_(r)- where r is an integer having a value of from 1 to 5 and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom; and where Y₅ and Y₆ when taken together represent the group ═CR₄R₅ where R₄ and R₅, which may be the same or different, are each selected from the group consisting of hydrogen and Y₃, with the proviso that R₄ and R₅ cannot be a hydroxyl; and where R4 and Y₂ when taken together may represent the group —(CR₁R₂)_(s)- where s is an integer having a value of from 1 to 3; and where the group R represents any of the typical side chains known for vitamin D type compounds.

[0023] More specifically R can represent a saturated or unsaturated hydrocarbon radical of 1-35 carbons, that may be straight-chain, branched or cyclic and that may contain one or more additional substituents, such as hydroxy- or protected-hydroxy groups, fluoro, carbonyl, ester, epoxy, amino or other heteroatomic groups. Preferred side chains of this type are represented by the structure below

[0024] where the stereochemical center (corresponding to C-20 in steroid numbering) may have the R or S configuration, (i.e. either the natural configuration about carbon 20 or the 20-epi configuration), and where Z is selected from Y, —OY, CH₂OY, —C≡CY and —CH═CHY, where the double bond may have the cis or trans geometry, and where Y is selected from hydrogen, methyl, —COR₁₀ and a radical of the structure:

[0025] where x and y, independently, represent the integers from 0 to 5, where R₆ is selected from hydrogen, deuterium, hydroxy, protected hydroxy, fluoro, trifluoromethyl, and C₁₋₅-alkyl, which may be straight chain or branched and, optionally, bear a hydroxy or protected-hydroxy substituent, and where each of R₇, R₈, and R₉, independently, is selected from deuterium, deuteroalkyl, hydrogen, fluoro, trifluoromethyl and C₁₋₅ alkyl, which may be straight-chain or branched, and optionally, bear a hydroxy or protected-hydroxy substituent, and where R₆ and R₇, taken together, represent an oxo group, or an alkylidene group, ═CR₇R₈, or the group —(CH₂)_(p)-, where p is an integer from 2 to 5, and where R₈ and R₉, taken together, represent an oxo group, or the group —(CH₂)_(q)-, where q is an integer from 2 to 5, and where R₁₀ represents hydrogen, hydroxy, protected hydroxy, or C₁₋₅ alkyl and wherein any of the CH-groups at positions 20, 22, or 23 in the side chain may be replaced by a nitrogen atom, or where any of the groups —CH(CH₃)—, —CH(R³)—, or —CH(R²)— at positions 20, 22, and 23, respectively, may be replaced by an oxygen or sulfur atom.

[0026] The wavy line to the substituent at C-20 indicates that the carbon 20 may have either the R or S configuration.

[0027] Specific important examples of side chains with natural 20R-configuration are the structures represented by formulas (a), (b), (c), (d) and (e) below, i.e. the side chain as is occurs in 25-hydroxyvitamin D₃ (a); vitamin D₃ (b); 25-hydroxyvitamin D₂ (c); vitamin D₂ (d); and the C-24 epimer of 25-hydroxyvitamin D₂ (e):

[0028] The above novel compounds wherein the 1α-OH group is presented in the axial orientation exhibit a desired, and highly advantageous, pattern of biological activity. These compounds are characterized by having greater biological activity, as compared to 1α,25(OH)₂D₃, in one or more of the three activities typically referred to as “calcemic” activities, i.e. intestinal calcium transport activity, bone mineralization activity and bone calcium mobilization activity, or in cell differentiation activity. Hence, these compounds may be highly specific in their calcemic activity. Their preferential calcemic activity suggests the in vivo administration of these compounds for the treatment of metabolic bone diseases where bone loss is a major concern. Because of their preferential calcemic activity on bone, one or more of these compounds may be preferred therapeutic agents for the treatment of diseases where bone formation is desired, such as osteoporosis, especially low bone turnover osteoporosis, steroid induced osteoporosis, senile osteoporosis or postmenopausal osteoporosis, as well as hypoparathroidism, osteomalacia and renal osteodystrophy. In addition, hypocalcemia as well as rickets, and vitamin D resistant rickets may be treated with one or more of the disclosed compounds. These compounds may also provide a method of treating female infertility in female mammals. The treatment may be transdermal, oral (in solid or liquid form) or parenteral. The compounds may be present in a composition in an amount from about 0.01 μg/day to about 100 μg/day, preferably about 0.1 μg/gm to about 50 μg/gm of the composition, and may be administered in dosages of from about 0.1 μg/day to about 50 μg/day.

[0029] The compounds of the invention are also especially suited for treatment and prophylaxis of human disorders which are characterized by an imbalance in the immune system, e.g. in autoimmune diseases, including multiple sclerosis, diabetes mellitus, host versus graft reaction, and rejection of transplants; and additionally for the treatment of inflammatory diseases, such as rheumatoid arthritis and asthma, as well as the improvement of bone fracture healing and improved bone grafts. Acne, alopecia, skin conditions such as dry skin (lack of dermal hydration), undue skin slackness (insufficient skin firmness), insufficient sebum secretion and wrinkles, and hypertension are other conditions which may be treated with one or more of the compounds of the invention.

[0030] The above compounds may also be characterized by high cell differentiation activity. Thus, these compounds may also provide therapeutic agents for the treatment of psoriasis and other skin disorders characterized by proliferation of undifferentiated skin cells, e.g. dermatitis, eczema, solar keratosis and the like, or as an anti-cancer agent, especially against leukemia, colon cancer, breast cancer and prostate cancer. The compounds may be present in a composition to treat disorders such as psoriasis in an amount from about 0.01 μg/gm to about 100 μg/gm of the composition, and may be administered topically, transdermally, orally (in solid or liquid form) or parenterally in dosages of from about 0.01 μg/day to about 100 μg/day.

[0031] This invention also provides a novel method of modifying or altering the structure of a 1α-hydroxylated vitamin D compound to increase its biological activity by altering the conformational equilibrium of the A-ring of the 1α-hydroxylated vitamin D compound to favor a chair conformation that presents the 1α-hydroxyl in the axial orientation. This is accomplished by either locking the chair conformation of the A-ring in a geometry having an axially orientated 1α-hydroxyl, or by the addition of one or more substituents to the A-ring which interact with other substituents in the molecule or on the A-ring to provide a driving force to the A-ring to adopt a chair conformation which presents the 1α-hydroxyl in the axial orientation.

DETAILED DESCRIPTION OF THE INVENTION

[0032] As used in the description and in the claims, the term “hydroxy-protecting group” signifies any group commonly used for the temporary protection of hydroxy functions, such as for example, alkoxycarbonyl, acyl, alkylsilyl or alkylarylsilyl groups (hereinafter referred to simply as “silyl” groups), and alkoxyalkyl groups. Alkoxycarbonyl protecting groups are alkyl-O—CO— groupings such as methoxycarbonyl, ethoxycarbonyl, propoxycarbonyl, isopropoxycarbonyl, butoxycarbonyl, isobutoxycarbonyl, tert-butoxycarbonyl, benzyloxycarbonyl or allyloxycarbonyl. The term “acyl” signifies an alkanoyl group of 1 to 6 carbons, in all of its isomeric forms, or a carboxyalkanoyl group of 1 to 6 carbons, such as an oxalyl, malonyl, succinyl, glutaryl group, or an aromatic acyl group such as benzoyl, or a halo, nitro or alkyl substituted benzoyl group. The word “alkyl” as used in the description of the claims, denotes a straight-chain or branched alkyl radical of 1 to 10 carbons, in all its isomeric forms. Alkoxyalkyl protecting groups are groupings such as methoxymethyl, ethoxymethyl, methoxyethoxymethyl, or tetrahydrofuiranyl and tetrahydropyranyl. Preferred silyl-protecting groups are trimethylsilyl, triethylsilyl, t-butyldimethylsilyl, dibutylmethylsilyl, diphenylmethylsilyl, phenyldimethylsilyl, diphenyl-t-butylsilyl and analogous alkylated silyl radicals. The term “aryl” specifies a phenyl-, or an alkyl-, nitro- or halo-substituted phenyl group.

[0033] A “protected hydroxy” group is a hydroxy group derivatised or protected by any of the above groups commonly used for the temporary or permanent protection of hydroxy functions, e.g. the silyl, alkoxyalkyl, acyl or alkoxycarbonyl groups, as previously defined. The terms “hydroxyalkyl”, “deuteroalkyl”, “aminoalkyl”, “halogenalkyl”, “alkoxyalkyl”, “aryloxyalkyl”, and “fluoroalkyl” refer to an alkyl radical substituted by one or more hydroxy, deuterium, amino, halogen, alkoxy, aryloxy, or fluoro group respectively. A “halogen” group includes any of the five elements fluorine, chlorine, bromine, iodine and astatine that form a part of group VIIA of the periodic table.

[0034] As previously discussed, the novel analogs of the present invention are characterized by the general formula I shown below:

[0035] where the definitions of Y₁, Y₂, Y₃, Y₄, Y₅, Y₆, Y₇, Y₈ and R are as previously set forth herein. The preferred analogs are the following:

[0036] 1 . 2-Substituted 1α-Hydroxy Vitamin D Compounds

[0037] 1.1. 2α-Substitution

[0038] Vitamins possessing 2α-substituent U that is characterized by large conformational free energy (A value) and, therefore having this C(2) substituent in equatorial disposition and, therefore, having 1α-hydroxyl in an axial orientation:

[0039] where U is selected from the group consisting of a methyl, a substituted methyl group described by general formula CR₁R₂R₃, an amino group or substituted amino group described by general formula NR₁R₂, a phosphino group or substituted phosphino group described by general formula PR₁R₂, an alkyl or arylsulfinyl group, an alkyl- or arylsulfonyl group, and aryl, and where R₁, R₂ and R₃ are each independently selected from the group consisting of hydrogen, alkyl, hydroxyalkyl, aminoalkyl, halogenalkyl, alkoxyalkyl, aryloxyalkyl, aryl, halogen, hydroxyl, protected hydroxy, alkoxyl, aryloxyl, acyl, an amino group, an amino group substituted with alkyl or aryl substitutents and where R₁ and R₂, taken together, represent an oxo group, or a group —(CH₂)_(m)- where m is an integer having a value of from 2 to 5.

[0040] 1.2. 2α-Substitution and Formation of a Ring with 3β-O

[0041] Vitamins that contain an anchoring bond system, i.e., possessing an additional ring connecting C(2) with C(3)—O. The vitamins are characterized by trans-diequatorial orientation of substituents at C(2) and C(3) and, therefore, they have 1α-hydroxyl in an axial orientation.

[0042] where R₁ and R₂ are as described above, and wherein n is an integer having a value of from 1 to 4, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.

[0043] 1.3. 2-Alkylidene Compounds

[0044] Vitamins in which 2-methylene group is further substituted by U. The vitamins are characterized by cis-orientation of substituents of the terminal olefinic atoms of the 1,4-dimethylenecyclohexane system of the ring A, i.e. cis-orientation between C(6)-C(7) bond and C(1′)—U bond. Substituent U due to its size strongly interacts with equatorial 1α-OH and, therefore, the inverted A-ring chair conformer is favored, having 1α-hydroxyl in an axial orientation:

[0045] where U is as described above with the proviso that U cannot be an —OH group.

[0046] 1.4. 2-Alkylidene Compounds with an Additional Connection with 3β-O.

[0047] Vitamins that contain a flattening bond system, i.e., an exocyclic 2-methylene group that is farther substituted and forms a ring with C(3)—O. The vitamins are characterized by trans-orientation of substituents of the terminal olefinic atoms of the 1,4-dimethylenecyclohexane system of the ring A, i.e., trans-orientation between C(6)-C(7) bond and C(1′)-C(2′)R₁R₂ bond. Therefore, these vitamins have C(3)—O substituent in equatorial disposition and 1α-hydroxyl in an axial orientation:

[0048] where R₁ and R₂ are as described above, and wherein s is an integer having a value of from 1 to 3, and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.

[0049] 2. 4α-Substitution and Formation of a Ring with 3β-O

[0050] Vitamins that contain an anchoring bond system, i.e., possessing an additional ring connecting C(4) with C(3)—O. The vitamins are characterized by trans-diequatorial orientation of substituents at C(3) and C(4) and, therefore, they have 1α-hydroxyl in an axial orientation:

[0051] where R₁ and R₂ are as described above, and wherein n is an integer having a value of from I to 4, and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.

[0052] 3. 10β-Substitution

[0053] Vitamins possessing 10β-substituent U, which due to its size strongly interacts with C(7)—H and, therefore, the inverted A-ring chair conformer is favored, having 1α-hydroxyl in an axial orientation:

[0054] where U is as described previously.

[0055] 4. 1,3-Diaxially Bridged Compounds

[0056] 4.1. 2β,4β-Bridged

[0057] Vitamins that contain a bridged bond system, i.e., possessing an additional ring connecting C(2) with C(4). The vitamins are characterized by cis-1,3-diaxial orientation of additional substituents at C(2) and C(4) and, therefore, they have 1α-hydroxyl in an axial orientation:

[0058] where R₁ and R₂ are as described above, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.

[0059] 4.2. 2β,10β-Bridged

[0060] Vitamins that contain a bridged bond system, i.e., possessing an additional ring connecting C(2) with C(10). The vitamins are characterized by cis-1,3-diaxial orientation of substituents at C(2) and C(10) and, therefore, they have 1α-hydroxyl in an axial orientation:

[0061] where R₁ and R₂ are as described above, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.

[0062] 4.3 4β,10β-Bridged

[0063] Vitamins that contain a bridged bond system, i.e., possessing an additional ring connecting C(4) with C(10). The vitamins are characterized by cis-1,3-diaxial orientation of additional substituents at C(4) and C(10) and, therefore, they have 1α-hydroxyl in an axial orientation:

[0064] where R₁ and R₂ are as described above, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.

[0065] Methods of making compounds of formulae I and 1.1-4.3 are known. Specifically, reference is made to Zhu et al, Chem. Rev. 95, 1877 (1995) and Dai et al, Synthesis 1383 (1994) which describe a method of synthesizing such compounds.

[0066] It should be noted in this description that the term “24-homo” refers to the addition of one methylene group and the term “24-dihomo” refers to the addition of two methylene groups at the carbon 24 position in the side chain. Likewise, the term “trihomo” refers to the addition of three methylene groups. Also, the term “26,27-dimethyl” refers to the addition of a methyl group at carbon 26 and 27 positions so that for example R³ and R⁴ are ethyl groups. Likewise, the term “26,27-diethyl” refers to the addition of an ethyl group at the 26 and 27 positions so that R³ and R⁴ are propyl groups.

[0067] In the following lists of compounds, the particular substituents attached on the A-ring should be added to the nomenclature. For example, if a methyl group is the alkyl substituent attached at the carbon 2 position on the A-ring, the term “2-methyl” should precede each of the named compounds. If an ethyl group is the alkyl substituent attached at the carbon 2 position on the A-ring, the term “2-ethyl” should precede each of the named compounds, and so on. In addition, if the methyl group attached at the carbon 20 position is in its epi or unnatural configuration, the term “20(S)” or “20-epi” should be included in each of the following named compounds. The named compounds could also be of the vitamin D₂ type if desired.

[0068] Specific and preferred examples of the compounds of structure I when the side chain is unsaturated are:

[0069] 1 9-nor-24-homo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0070] 19-nor-24-dihomo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0071] 19-nor-24-trihomo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0072] 19-nor-26,27-dimethyl-24-homo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0073] 19-nor-26,27-dimethyl-24-dihomo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0074] 19-nor-26,27-dimethyl-24-trihomo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0075] 19-nor-26,27-diethyl-24-homo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0076] 19-nor-26,27-diethyl-24-dihomo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0077] 19-nor-26,27-diethyl-24-trihomo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0078] 19-nor-26,27-dipropyl-24-homo-1,25-dihydroxy-22-dehydrovitamin D₃;

[0079] 19-nor-26,27-dipropyl-24-dihomo-1,25-dihydroxy-22-dehydrovitamin D₃; and

[0080] 9-nor-26,27-dipropyl-24-trihomo- 1,25-dihydroxy-22-dehydrovitamin D₃.

[0081] Specific and preferred examples of the compounds of structure I when the side chain is saturated are:

[0082] 19-nor-24-homo-1,25dihydroxyvitamin D₃;

[0083] 19-nor-24-dihomo-1,25-dihydroxyvitamin D₃;

[0084] 19-nor-24-trihomo-1,25-dihydroxyvitamin D₃;

[0085] 19-nor-26,27-dimethyl-24-homo-1,25-dihydroxyvitamin D₃;

[0086] 19-nor-26,27-dimethyl-24-dihomo-1,25-dihydroxyvitamin D₃;

[0087] 19-nor-26,27-dimethyl-24-dihomo- 1,25-dihydroxyvitamin D₃;

[0088] 19-nor-26,27-diethyl-24-homo-1,25-dihydroxyvitamin D₃;

[0089] 19-nor-26,27-diethyl-24-dihomo-1,25-dihydroxyvitamin D₃;

[0090] 19-nor-26,27-diehtyl-24-trihomo-1,25-dihydroxyvitamin D₃;

[0091] 19-nor-26,27-dipropyl-24-homo-1,25-dihydroxyvitamin D₃;

[0092] 19-nor-26,27-dipropyl-24-dihomo-1,25-dihydroxyvitamin D₃; and

[0093] 19-nor-26,27-dipropyl-24-trihomo-1,25-dihydroxyvitamin D₃.

[0094] For treatment purposes, the novel compounds of this invention defined by formula I may be formulated for pharmaceutical applications as a solution in innocuous solvents, or as an emulsion, suspension or dispersion in suitable solvents or carriers, or as pills, tablets or capsules, together with solid carriers, according to conventional methods known in the art. Any such formulations may also contain other pharmaceutically-acceptable and non-toxic excipients such as stabilizers, anti-oxidants, binders, coloring agents or emulsifying or taste-modifying agents.

[0095] The compounds may be administered orally, topically, parenterally or transdermally. The compounds are advantageously administered by injection or by intravenous infusion or suitable sterile solutions, or in the form of liquid oral doses or solid doses via the alimentary canal, or in the form of creams, ointments, patches, or similar vehicles suitable for transdermal applications. Doses of from 0.01 μg to 100 μg per day, preferably 0.1 μg to 50 μg per day, of the compounds are appropriate for treatment purposes, such doses being adjusted according to the disease to be treated, its severity and the response of the subject as is well understood in the art. Since the new compounds exhibit specificity of action, each may be suitably administered alone, or together with graded doses of another active vitamin D compound—e.g. 1α-hydroxyvitamin D₂ or D₃, or 1α,25-dihydroxyvitamin D₃—in situations where different degrees of bone mineral mobilization and calcium transport stimulation is found to be advantageous.

[0096] Compositions for use in the above-mentioned cell differentiation treatments, e.g. psoriasis and other malignancies comprise an effective amount of one or more vitamin D compound as defined by the above formula I as the active ingredient, and a suitable carrier. An effective amount of such compounds for use in accordance with this invention is from about 0.01 μg to about 100 μg per gm of composition, and may be administered topically, transdermally, orally or parenterally in dosages of from about 0.1 μg/day to about 100 μg/day.

[0097] The compounds may be formulated as creams, lotions, ointments, topical patches, pills, capsules or tablets, or in liquid form as solutions, emulsions, dispersions, or suspensions in pharmaceutically innocuous and acceptable solvents or oils, and such preparations may contain in addition other pharmaceutically innocuous or beneficial components, such as stabilizers, antioxidants, emulsifiers, coloring agents, binders or taste-modifying agents.

[0098] The compounds are advantageously administered in amounts sufficient to effect the differentiation of promyelocytes to normal macrophages. Dosages are described above are suitable, it being understood that the amounts given are to be adjusted in accordance with the severity of the disease, and the condition and response of the subject as is well understood in the art.

[0099] The formulations of the present invention comprise an active ingredient in association with a pharmaceutically acceptable carrier therefore and optionally other therapeutic ingredients. The carrier must be “acceptable” in the sense of being compatible with the other ingredients of the formulations and not deleterious to the recipient thereof.

[0100] Formulations of the present invention suitable for oral administration may be in the form of discrete units as capsules, sachets, tablets or lozenges, each containing a predetermined amount of the active ingredient; in the form of a powder or granules; in the form of a solution or a suspension in an aqueous liquid or non-aqueous liquid; or in the form of an oil-in-water emulsion or a water-in-oil emulsion.

[0101] Formulations for rectal administration may be in the form of a suppository incorporating the active ingredient and a carrier such as cocoa butter, or in the form of an enema.

[0102] Formulations suitable for parenteral administration conveniently comprise a sterile oily or aqueous preparation of the active ingredient which is preferably isotonic with the blood of the recipient.

[0103] Formulations suitable for topical administration include liquid or semi-liquid preparations such as liniments, lotions, applicants, oil-in-water or water-in-oil emulsions such as creams, ointments or pastes; or solutions or suspensions such as drops; or as sprays.

[0104] For asthma treatment, inhalation of powder, self-propelling or spray formulations, dispensed with a spray can, a nebulizer or an atomizer can be used. The formulations, when dispensed, preferably have a particle size in the range of 10 to 100μ.

[0105] The formulations may conveniently be presented in dosage unit form and may be prepared by any of the methods well known in the art of pharmacy. The term “dosage unit” is meant a unitary, i.e. a single dose which is capable of being administered to a patient as a physically and chemically stable unit dose comprising either the active ingredient as such or a mixture of it with solid or liquid pharmaceutical diluentes or carriers.

[0106] In its broadest application, the present invention relates to any analog of vitamin D which have the vitamin D nucleus. By “vitamin D nucleus”, it is meant a central part consisting of a substituted chain of five carbon atoms which correspond to positions 8, 14, 13, 17 and 20 of vitamin D₃ and at the ends of which are connected at position 20 a structural moiety representing any of the typical side chains known for vitamin D type compounds (such as R as previously defined herein), and at position 8 the 5,7-diene moiety connected to the A-ring of an active 1α-hydroxy vitamin D analog (as illustrated by formula I herein). Thus, various known modifications to the six-membered C-ring and the five-membered D-ring typically present in vitamin D₃ such as the lack of one or the other or both, are also embraced by the present invention.

[0107] Accordingly, compounds of the following formulae Ia, are along with those of formula I, also encompassed by the present invention:

[0108] In the above formula Ia, the definitions of Y₁, Y₂, Y₃, Y₄, Y₅, Y₆, Y₇, Y₈ and Z are as previously set forth herein. With respect to X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈ and X₉, these substituents may be the same or different and are selected from hydrogen or lower alky, i.e. a C₁₋₅ alkyl such as methyl, ethyl or n-propyl. In addition, paired substituents X₁ and X₄ or X₅, X₂ or X₃ and X₆ or X₇, X₄ or X₅ and X₈ or X₉, when taken together with the three adjacent carbon atoms of the central part of the compound, which correspond to positions 8, 14, 13 or 14, 13, 17 or 13, 17, 20 respectively, can be the same or different and form a saturated or unsaturated, substituted or unsubstituted, carbocyclic 3, 4, 5, 6 or 7 membered ring.

[0109] Preferred compounds of the present invention may be represented by one of the following formulae:

[0110] In the above formulae Ib, Ic, Id, Ie, If, Ig and Ih, the definitions of Y₁, Y₂, Y₃, Y₄, Y₅, Y₆, Y₇Y₈, R, Z, X₁, X₂, X₃, X₄, X₅, X₆, X₇ and X₈ are as previously set forth herein. The substituent Q represents a saturated or unsaturated, substituted or unsubstituted, hydrocarbon chain comprised of 0, 1, 2, 3 or 4 carbon atoms, but is preferably the group —(CH₂)_(k)- where k is an integer equal to 2 or 3.

[0111] Methods for making compounds of formulae Ia-Ih are known. Specifically, reference is made to International Application Number PCT/EP94/02294 filed Jul. 7, 1994 and published Jan. 19, 1995 under International Publication Number WO95/01960. 

We claim:
 1. A method of modifying the calcemic activity of a 1α-hydroxylated vitamin D compound to increase in vivo activity, comprising: altering the conformational equilibrium of the A-ring of a 1α-hydroxylated vitamin D compound to favor a chair conformation for said A-ring that presents the 1α-hydroxyl in an axial orientation.
 2. The method of claim 1 wherein the step of altering conformational equilibrium comprises locking the chair conformation of the A-ring in a geometry having an axially orientated 1α-hydroxyl.
 3. The method of claim 2 wherein the step of locking comprises adding an anchoring bond system to the A-ring.
 4. The method of claim 3 wherein the anchoring bond system comprises substituents attached to carbon 2 and carbon 3 of the A-ring that have a trans-diequatorial orientation.
 5. The method of claim 3 wherein the A-ring and anchoring bond system has the following structure:

where R₁ and R₂ are as described above, and wherein n is an integer having a value of from 1 to 4, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 6. The method of claim 3 wherein the anchoring bond system comprises substituents attached to carbon 3 and carbon 4 of the A-ring that have a trans-diequatorial orientation.
 7. The method of claim 3 wherein the A-ring and anchoring bond system has the following structure:

where R₁ and R₂ are as described above, and wherein n is an integer having a value of from 1 to 4, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 8. The method of claim 2 wherein the step of locking comprises adding a flattening bond system to the A-ring.
 9. The method of claim 8 wherein the A-ring and flattening bond system has the following structure:

where R₁ R₂ are as described above, and wherein s is an integer having a value of from 1 to 3, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 10. The method of claim 2 wherein the step of locking comprises adding a bridged bond system to the A-ring.
 11. The method of claim 10 wherein the bridged bond system comprises substituents attached to carbon 2 and carbon 4 of the A-ring that have a cis-1,3-diaxial orientation.
 12. The method of claim 10 wherein the A-ring and bridged bond system has the following structure:

where R₁ and R₂ are as described above, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 13. The method of claim 10 wherein the bridged bond system comprises substituents attached to carbon 2 and carbon 10 of the A-ring that have a cis-1,3 -diaxial orientation.
 14. The method of claim 10 wherein the A-ring and bridged bond system has the following structure:

where R₁ and R₂ are as described above, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 15. The method of claim 10 wherein the bridged bond system comprises substituents attached to carbon 4 and carbon 10 of the A-ring that have a cis-1,3-diaxial orientation.
 16. The method of claim 10 wherein the A-ring and the bridged bond system has the following structure:

where R₁ and R₂ are as described above, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 17. The method of claim 1 wherein the step of altering conformational equilibrium comprises modifying the A-ring by the addition of one or more substituents which interacts with other substituents on the A-ring to provide a driving force to the A-ring to adopt a chair conformation which presents the 1α-hydroxyl in said axial orientation.
 18. The method of claim 17 wherein the substituent attached to carbon 2 of the A-ring has a conformational free energy value greater than about 1.4 kcal/mol and the carbon 2 substituent has an equatorial orientation.
 19. The method of claim 17 wherein the A-ring has the following structure:

where U is selected from the group consisting of a methyl, a substituted methyl group described by general formula CR₁R₂R₃, an amino group or substituted amino group described by general formula NR₁R₂, a phosphino group or substituted phosphino group described by general formula PR₁R₂, an alkyl- or arylsulfinyl group, an alkyl- or arylsulfonyl group, and aryl, and where R₁, R₂ and R₃ are each independently selected from the group consisting of hydrogen, alkyl, hydroxyalkyl, aminoalkyl, halogenalkyl, alkoxyalkyl, aryloxyalkyl, aryl, halogen, hydroxyl, protected hydroxy, alkoxyl, aryloxyl, acyl, an amino group, an amino group substituted with alkyl or aryl substituents and where R₁ and R₂, taken together, represent an oxo group, or a group —(CH₂)_(m)- where m is an integer having a value of from 2 to
 5. 20. The method of claim 17 wherein the A-ring has the following structure:

where U is as described in claim 19 with the proviso that U cannot be an —OH group.
 21. The method of claim 17 wherein the substituent attached to carbon 10 of the A-ring has a conformational free energy value greater than about 1.4 kcal/mol and the carbon 10 substituent has an axial orientation.
 22. The method of claim 17 wherein the A-ring has the following structure:

where U is as described in claim
 19. 23. A method of increasing the biological response of a 1α-hydroxylated vitamin D compound comprising evaluating the conformational equilibrium of the A-ring of a 1α-hydroxylated vitamin D compound to determine to what extent said 1α-hydroxyl is presented axially or equatorially; and if presented primarily equatorially, modifying the A-ring by the addition of a substituent thereto which locks said A-ring in a chair conformation that maintains the 1α-hydroxyl in said axial orientation; or modifying the A-ring by the addition of a substituent thereto which provides a driving force to the A-ring to adopt a chair conformation which presents the 1α-hydroxyl in said axial orientation.
 24. The method of claim 23 wherein the step of modifying the A-ring comprises adding an anchoring bond system to the A-ring.
 25. The method of claim 24 wherein the anchoring bond system is added between substituents attached to carbons 2 and 3 of the A-ring.
 26. The method of claim 24 wherein the anchoring bond system is added between substituents attached to carbons 3 and 4 of the A-ring.
 27. The method of claim 23 wherein the step of modifying the A-ring comprises adding a flattening bond system to the A-ring.
 28. The method of claim 27 wherein the flattening bond system is added between substituents attached to carbons 2 and 3 of the A-ring.
 29. The method of claim 23 wherein the step of modifying the A-ring comprises adding a bridged bond system to the A-ring.
 30. The method of claim 29 wherein the bridged bond system is added between substituents attached to carbons 2 and 4 of the A-ring.
 31. The method of claim 29 wherein the bridged bond system is added between substituents attached to carbons 2 and 10 of the A-ring.
 32. The method of claim 29 wherein the bridged bond system is added between substituents attached to carbons 4 and 10 of the A-ring.
 33. The method of claim 23 wherein the step of modifying the A-ring comprises adding a substituent to carbon 2 of the A-ring having a conformational free energy value greater than about 1.4 kca/mol.
 34. The method of claim 23 wherein the step of modifying the A-ring comprises adding a substituent to carbon 10 of the A-ring having a conformational free energy value greater than about 1.4 kcal/mol.
 35. A compound having the formula:

where Y₁ and Y₂, which may be the same or different, are each selected from the group consisting of hydrogen and a hydroxy-protecting group; where Y₃, Y₄, Y₅, Y₆, Y₇ and Y₈, which may be the same or different, are each selected from the group consisting of hydrogen, a methyl group or substituted methyl group of the formula —CR₁R₂R₃, an amino group or substituted amino group of the formula —NR₁R₂, a phosphino group or substituted phosphino group of the formula —PR₁R₂, an alkylsulfinyl group, an arylsulfinyl group, an alkylsulfonyl group, an arylsulfonyl group, and aryl, where R₁, R₂ and R₃ are each independently selected from the group consisting of hydrogen, C₁₋₅ alkyl, hydroxyalkyl, aminoalkyl, halogenalkyl, alkoxyalkyl, aryloxyalkyl, aryl, halogen, hydroxyl, protected hydroxy, alkoxyl, aryloxyl, acyl, an amino group, an alkyl substituted amino group, and an aryl substituted amino group, and where R₁ and R₂ taken together represent an oxo group or a group —(CH₂)_(m)- where m is an integer having a value of from 2 to 5; or Y₃ and Y₄ when taken together represent a methylene group; or Y₇ and Y₈ when taken together represent a methylene group; where Y₂ and Y₆, or Y₂ and Y₇, when taken together may represent the group —(CR₁R₂)_(n)- where n is an integer having a value of from 1 to 4 and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom; where Y₅ and Y₈, or Y₅ and Y₃, or Y₃ and Y₈, when taken together may represent the group —(CR₁R₂)_(r)- where r is an integer having a value of from 1 to 5 and wherein any of the groups —CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom; and where Y₅ and Y₆ when taken together represent the group ═CR₄R₅ where R₄ and R₅, which may be the same or different, are each selected from the group consisting of hydrogen and Y₃ with the proviso that R₄ and R₅ cannot be a hydroxyl; and where R₄ and Y₂ when taken together may represent the group —(CR₁R₂),- where s is an integer having a value of from 1 to 3; and R is represented by the structure below

where the stereochemical center at carbon 20 may have the R or S configuration, and where Z is selected from Y, —OY, —CH₂OY, —C≡CY and —CH═CHY, where the double bond may have the cis or trans geometry, and where Y is selected from hydrogen, methyl, —COR₁₀ and a radical of the structure:

where x and y, independently, represent the integers from 0 to 5, where R₆ is selected from hydrogen, deuterium, hydroxy, protected hydroxy, fluoro, trifluoromethyl, and C₁₋₅-alkyl, which may be straight chain or branched and, optionally, bear a hydroxy or protected-hydroxy substituent, and where each of R₇, R₈, and R₉, independently, is selected from deuterium, deuteroalkyl, hydrogen, fluoro, trifluoromethyl and C₁₋₅ alkyl, which may be straight-chain or branched, and optionally, bear a hydroxy or protected-hydroxy substituent, and where R₆ and R₇, taken together, represent an oxo group, or an alkylidene group, ═CR₇R₈, or the group —(CH₂)_(p)-, where p is an integer from 2 to 5, and where R₈ and R₉, taken together, represent an oxo group, or the group —(CH₂)_(q)-, where q is an integer from 2 to 5, and where R₁₀ represents hydrogen, hydroxy, protected hydroxy, or C₁₋₅ alkyl and wherein any of the CH-groups at positions 20, 22, or 23 in the side chain may be replaced by a nitrogen atom, or where any of the groups —CH(CH₃)—, —CH(R³)—, or —CH(R²)— at positions 20, 22, and 23, respectively, may be replaced by an oxygen or sulfur atom.
 36. The compound of claim 35 having the formula:

where U is selected from the group consisting of a methyl, a substituted methyl group described by general formula CR₁R₂R₃, an amino group or substituted amino group described by general formula NR₁R₂, a phosphino group or substituted phosphino group described by general formula PR₁R₂, an alkyl- or arylsulfinyl group, an alkyl- or arylsulfonyl group, and aryl, and where R₁, R₂ and R₃ are each independently selected from the group consisting of hydrogen, alkyl, hydroxyalkyl, aminoalkyl, halogenalkyl, alkoxyalkyl, aryloxyalkyl, aryl, halogen, hydroxyl, protected hydroxy, alkoxyl, aryloxyl, acyl, an amino group, an amino group substituted with alkyl or aryl substituents and where R₁ and R₂, taken together, represent an oxo group, or a group —(CH₂)_(m)- where m is an integer having a value of from 2 to
 5. 37. The compound of claim 35 having the formula:

where R₁ and R₂ are as described in claim 36, and wherein n is an integer, having a value of from 1 to 4, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 38. The compound of claim 35 having the formula:

where U is as described in claim 36 with the proviso that U cannot be an —OH group.
 39. The compound of claim 35 having the formula:

where R₁ and R₂ are as described in claim 36, and wherein s is an integer having a value of from 1 to 3, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 40. The compound of claim 35 having the formula:

where R₁ and R₂ are as described in claim 36, and wherein n is an integer having a value of from 1 to 4, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 41. The compound of claim 35 having the formula:

where U is as described in claim
 36. 42. The compound of claim 35 having the formula:

where R₁ and R₂ are as described in claim 36, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 43. The compound of claim 35 having the formula:

where R₁ and R₂ are as described in claim 36, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 44. The compound of claim 35 having the formula:

where R₁ and R₂ are as described in claim 36, and wherein r is an integer having a value of from 1 to 5, and wherein any of the groups CR₁R₂- may be replaced by an oxygen, sulfur or nitrogen atom.
 45. A pharmaceutical composition containing an effective amount of at least one compound as claimed in claim 35 together with a pharmaceutically acceptable excipient.
 46. The pharmaceutical composition of claim 45 in dosage unit form.
 47. The pharmaceutical composition of claim 46 containing about 0.01 μg to about 100 μg of said at least one compound.
 48. The pharmaceutical composition of claim 45 in topical form.
 49. The pharmaceutical composition of claim 45 in oral form.
 50. A method of treating metabolic bone disease where it is desired to maintain or increase bone mass comprising administering to a patient with said disease an effective amount of a compound as claimed in claim
 35. 51. The method of claim 50 where the disease is senile osteoporosis.
 52. The method of claim 50 where the disease is postmenopausal osteoporosis.
 53. The method of claim 50 where the disease is steroid-induced osteoporosis.
 54. The method of claim 50 where the disease is low bone turnover osteoporosis.
 55. The method of claim 50 where the disease is osteomalacia.
 56. The method of claim 50 where the disease is renal osteodystrophy.
 57. The method of claim 50 where the disease is rickets.
 58. The method of claim 50 where the disease is vitamin D resistant rickets.
 59. The method of claim 50 wherein the compound is administered orally.
 60. The method of claim 50 wherein the compound is administered parenterally.
 61. The method of claim 50 wherein the compound is administered transdermally.
 62. The method of claim 50 wherein the compound is administered in a dosage of from 0.1 μg to 50 μg per day.
 63. A method of treating a disease characterized by abnormal cell proliferation or cell differentiation comprising administering to a patient with said disease an effective amount of a compound as claimed in claim
 35. 64. The method of claim 63 where the disease is psoriasis.
 65. The method of claim 63 where the disease is a cancer selected from the group consisting of leukemia, colon cancer, breast cancer and prostate cancer.
 66. The method of claim 63 where the disease is a skin disorder selected from the group consisting of dermatitis, eczema and keratosis.
 67. A method of treating a disease characterized by an imbalance in the immune system comprising administering to a patient with said disease an effective amount of a compound as claimed in claim
 35. 68. The method of claim 67 where the disease is multiple sclerosis.
 69. The method of claim 67 where the disease is diabetes mellitus.
 70. The method of claim 67 where the disease is transplant rejection.
 71. A method of treating rheumatoid arthritis comprising administering to a patient with rheumatoid arthritis an effective amount of a compound as claimed in claim
 35. 72. A method of treating asthma comprising administering to a patient with asthma an effective amount of a compound as claimed in claim
 35. 73. A method of treating hypertension comprising administering to a patient with hypertension an effective amount of a compound as claimed in claim
 35. 74. A method of treating hypocalcemia comprising administering to a patient with hypocalcemia an effective amount of a compound as claimed in claim
 35. 75. A method of treating hypoparathroidism comprising administering to a patient with hypoparathroidism an effective amount of a compound as claimed in claim
 35. 76. A method of treating female infertility which comprises administering to a female mammal an effective amount of a compound as claimed in claim
 35. 77. A method of treating acne comprising administering to a patient with acne an effective amount of a compound as claimed in claim
 35. 78. A method of treating alopecia comprising administering to a patient with alopecia an effective amount of a compound as claimed in claim
 35. 79. A method of treating skin conditions selected from the group consisting of lack of skin firmness, wrinkles, lack of dermal hydration and insufficient sebum secretion which comprises administering to a patient by topical, oral or parenteral means an effective amount of a compound as claimed in claim
 35. 